Use the graph of ƒ (x) = x² below to find a number & such that x² − 1| < 0.5 whenever 0 < |ï − 1| < 8. 8 y = Number 1.5 1 0.5- Round your answer to four decimal places. 0 Maple plot 1 X

Q: 6. x³-x²-x+10 lim x-2 x² + 3x + 2

A:

Q: For the following exercise, find the volume generated when the region between the curves is rotated…

A: I am attaching image so that you understand each and every step.

Q: (2x+5)³(52²-2x) 4. Use logarithmic differentiation to find the derivative of the function y = √2x+5

A:

Q: The area of a square is increasing at a rate of 56 centimeters squared per second. Find the rate of…

A: Given data÷ Rate of change of area  =dAdt=56cm2/s Side of square =a=4cm We need to find dadt=?

Q: 5. (y4 - 2xy) dx + 3x² dy = 0; when x = 2, y = 1.

A:

Q: Aylindrical can has a volume of 167 cm³. Use Lagrange multipliers to determine the dimensions of the…

A:

Q: Let f be the function graphed below. If 20 subintervals of equal length are used, write a summation…

A:

Q: Solve for the X 10=[ (1+6x)/7]^5x/6

A: I am attaching image so that you understand each and every step.

Q: Evaluate the integral: (A) Which trig substitution is correct for this integral? 1 0x = -sec (0) 10…

A: The given integral is: ∫dx64-10x232 (B) To find: Which integral do you obtain after substituting for…

Q: 7. Find the equation of a normal to y = x³ - 3x²+x-1 at x = 3

A:

Q: b) 2 1/2 dx x(lnx)4

A: Topic:- integration

Q: 2 8. y' + ²y = -x²y² cos x

A:

Q: 2 area of region .25 and 2 Use horizontal strips to find the area, that is, integrate with respect…

A:

Q: 2. Consider the parallelogram ABCD where A(0,1,2), B(1,2,3), and C(0,3,5). [2] a) Find the…

A:

Q: Evaluate the definite integral. 1³ sin (4t)dt

A:

Q: Let the line PQ pass through the points P = (-4,-4, -6) and Q = (-2, 1, - 16). The line will pass…

A:

Q: Consider points A(4, -1, 3), B(3, 1, 6), and C(1, -3, -3). (a) Find the area of parallelogram ABCD…

A: The given problem is solved below in detail.

Q: ✓ ["1 [™ f(a)da - [* f(x)dx = - Sª f(x)dx and b where a = If what are the bounds of integration for…

A:

Q: esc Consider the vector field F = O The vector field is not conservative O The vector field is…

A:

Q: Find the second derivative of the vector-valued function r(t) = (4t+ 3 sin(t))i + (5t + 3 cos (t))…

A:

Q: Evaluate the following integral over the Region R. (Answer accurate to 4 significant places). SS R…

A: In this question, we need to evaluate the given integral.

Q: 1. Simplify the following: a) b) 8 45x X 3 15y 20y 18x 2 (x² − 9) 5 2 x+5x +6

A: Recall: a2-b2=(a+b)(a-b)

Q: Let r(t) = cost i + e^t j + t^2 k be given. A) Find the unit tangent vector to the curve at any…

A: Given: rt= cost i + et j + t2 k

Q: Solve (2y² + 3xy - 2y + 6x) dx + x (x + 2y - 1) dy=0 a. x² (y² + xy b. y + 2x) = C y² (y² + xy + y +…

A: Please see the below picture for detailed solution.

Q: Consider vectors u and v. Find unit vector w in the direction of the cross product vector u x v.…

A:

Q: d) f(a)= (2a-1)² 2a + 5a

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: 191. f(x) = x³ + 1

A:

Q: 1. Which of the following relations is a function? a) {(1,9), (2, 4), (2, 3), (4, 15)} {(2, 7), (7,…

A: Recall:  A function can be defined as a relation between "each of its inputs" to "exactly one…

Q: Evaluate the limit of the given functions. 3x17x+ 20 lim. x44x² 25x+36 1. 2. lim t3 - 1 고 t-it-1

A: "According to the guidelines issued by the company we are supposed to answer only first three…

Q: Find the area enclosed by the lemniscate with equation ² Choose your limits of integration…

A:

Q: 4. Which of the following is f(x) = x² the parent function for? a) f(x) = x³ + 2x²-x+ 13. b)…

A:

Q: You are taking a road trip in a car without A/C. The temperture in the car is 105 degrees F. You buy…

A: Above question is solved.

Q: Which of the following is the complete set of roots of the auxiliary equation fory"'' - 3y "' + 3y…

A:

Q: Differentiate the following function. You do not need to simplify the derivative. ƒ'(x) = 5 f(x) =…

A: Derivative of function f(x)=lnx5

Q: Solve the differential equation of dx (A) In y = c Inx

A: Given: dydx=ylnx

Q: sec¹ (3x) b) ›1$ 3 tan³ (3x) dx

A: I have stated the used formulas in the solution

Q: A tank half-filled with water is in the form of a rectangular parallelepiped 5 ft deep, 15 ft wide,…

A:

Q: 2 √9x²-16 x² dx

A: We will use substitute method to solve the integration

Q: er of cars produced when a dollars is spent on labor and y dollars is spent on capital invested by 1…

A: Topic:- application of derivatives

Q: Evaluate the Integral using the following values. [°x³ dx = 260, [°x dx = 10, [°dx = 2 [°(22-7x-x²)…

A:

Q: 4. The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6…

A:

Q: Assume the coordinates are integers. Determine the coordinates of the point shown. (Type an ordered…

A:

Q: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Set up the definite integral required to find the area of the region between the graph of y = 17 -…

A:

Q: 10. Explain what it means if a. 6 = 0

A:

Q: The differential equation dy x-2y+3 ax 2x+3y-4 = is reduced to [homogenous or separable

A:

Q: Find 2 -1 (3x³ + 7x¹) dx

A: Here we have to solve definite integral

Q: Use the graph of f (x): = Enter the exact answer. 1/1/00 below to find a number & such that |ƒ (x) -…

A: The objective is to find the value of delta.

Q: The function f is shown below. What is the value of answer in simplest form. -10 -9 -8 -7 -6 -5 4 3…

A:

Q: Find the exact average value fare of f(2)=√16-2² between 0 and 4, then find an exact number e in…

A: